Wave equation and multiplier estimates on Damek-Ricci spaces

Thumbnail Image

Date

Authors

Journal Title

Journal ISSN

Volume Title

Publisher

Abstract

Description

Let S be a Damek-Ricci space and L be a distinguished left invariant Laplacian on S. We prove pointwise estimates for the convolution kernels of spectrally localized wave operators associated with L. This generalizes previous results proved by D. Mueller and C. Thiele on ax+b-groups. We also prove pointwise estimates of the gradient of these convolution kernels. As a corollary we reprove basic multiplier estimates from previous papers of W. Hebisch and T. Steger and M. Vallarino by different methods. Finally we derive Sobolev estimates for the solution to the wave equation associated with L.

Keywords

Classical Analysis and ODEs, Analysis of PDEs, 43A15; 42B15; 22E30

Citation

URI

http://salesiana.dossiersoluciones.com/handle/123456789/163153

Consulte el texto completo en el siguiente enlace:

https://arxiv.org/abs/0806.2921
 http://arxiv.org/abs/0806.2921

Collections

arXiv